Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question
The equation given is \( g(x) = (x^4 - 2x)x^5 \). The task is to find \( g'(x) \), the derivative of the function \( g(x) \). ### Explanation: 1. **Function**: \( g(x) \) is expressed as a product of two functions: \( (x^4 - 2x) \) and \( x^5 \). 2. **Derivative Concepts**: To find the derivative \( g'(x) \), you'll likely use the product rule. The product rule states that if you have a function \( u(x) \cdot v(x) \), then the derivative is \( u'(x) v(x) + u(x) v'(x) \). 3. **Steps**: - Identify \( u(x) = x^4 - 2x \) and \( v(x) = x^5 \). - Compute the derivatives \( u'(x) \) and \( v'(x) \). - Apply the product rule to find \( g'(x) \).
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Transcribed Image Text:The equation given is \( g(x) = (x^4 - 2x)x^5 \). The task is to find \( g'(x) \), the derivative of the function \( g(x) \). ### Explanation: 1. **Function**: \( g(x) \) is expressed as a product of two functions: \( (x^4 - 2x) \) and \( x^5 \). 2. **Derivative Concepts**: To find the derivative \( g'(x) \), you'll likely use the product rule. The product rule states that if you have a function \( u(x) \cdot v(x) \), then the derivative is \( u'(x) v(x) + u(x) v'(x) \). 3. **Steps**: - Identify \( u(x) = x^4 - 2x \) and \( v(x) = x^5 \). - Compute the derivatives \( u'(x) \) and \( v'(x) \). - Apply the product rule to find \( g'(x) \).
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